New Integral Inequalities for the Nevanlinna Characteristics of Meromorphic Functions
- Md Mainul Islam
- A. N. M. Rezaul Karim
Abstract
In this paper, we introduce generalization of the Nevanlinna characteristics and give a short survey of classical and recent results on the representation of a meromorphic function in terms such characteristics. And then we characterize the counting functions N(r,f), N(r,a), and the characteristics functions T(r,f), T(r,a) defined on a non-constant meromorphic ( ). Besides this, we prove that the terms N(e^u,f), N(e^u,a), and T(e^u,f), T(e^u,a), are convex functions for any real values of u. Finally, we derive some integral inequalities depend on these terms, analogous to well known Hadamard’s inequality, by using elementary analysis.- Full Text:
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- DOI:10.5539/jmr.v7n3p99
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